This test has two parts: the first one is about 4 multiple-choice questions, 0.5 points per question; answer is worth 0.2 points, while the solving process is worth 0.3 points. In the second part, you must choose three out of the four proposed situations, showing your answer (0.3 points each) and all the solving path (0.7 points each).

This test is in pairs, previously arranged by the teacher, but the submission of all the work is individual. You are allowed to use only your own notebook and a scientific calculator. Cellphones are not allowed during all the test.

Part 1. Answer the following questions:The expression to calculate the conditional probability between A (the probable event) and B (the occurred event) is What is the condition that P(B) must fulfill?

In a library box, there are 8 novels, 8 biographies, and 8 war history books. If Jack selects two books at random, what is the probability of selecting two different kinds of books in a row?

16/23

16/24

8/24

7/23

A new superman MasterCard has been issued to 2000 customers. Of these customers, 1500 hold a Visa card, 500 hold an American Express card and 40 hold a Visa card and an American Express card. Find the probability that a customer chosen at random holds a Visa card, given that the customer holds an American Express card.

1/4

1/3

2/25

1/50

Part 2. Solve the provided problems1, showing all your work in an additional piece of paper. Remember to show the answer at the end (i.e. The distance between A and B is ____________):

Seventy percent of kids who visit a doctor have a fever and 30% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

You draw a card at random from a standard deck of cards. Find each of the following conditional probabilities:

In a monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the following conditional probabilities if an animal is selected at random: